50 ideas
| 8060 | In the 17th-18th centuries morality offered a cure for egoism, through altruism [MacIntyre] |
| 8053 | Twentieth century social life is re-enacting eighteenth century philosophy [MacIntyre] |
| 8047 | Philosophy has been marginalised by its failure in the Enlightenment to replace religion [MacIntyre] |
| 8062 | Proof is a barren idea in philosophy, and the best philosophy never involves proof [MacIntyre] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 8052 | To find empiricism and science in the same culture is surprising, as they are really incompatible [MacIntyre] |
| 8057 | Unpredictability doesn't entail inexplicability, and predictability doesn't entail explicability [MacIntyre] |
| 8054 | Social sciences discover no law-like generalisations, and tend to ignore counterexamples [MacIntyre] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 21050 | I can only make decisions if I see myself as part of a story [MacIntyre] |
| 8056 | AI can't predict innovation, or consequences, or external relations, or external events [MacIntyre] |
| 8059 | The good life for man is the life spent seeking the good life for man [MacIntyre] |
| 8034 | We still have the appearance and language of morality, but we no longer understand it [MacIntyre] |
| 8036 | Unlike expressions of personal preference, evaluative expressions do not depend on context [MacIntyre] |
| 8049 | Moral judgements now are anachronisms from a theistic age [MacIntyre] |
| 8045 | The failure of Enlightenment attempts to justify morality will explain our own culture [MacIntyre] |
| 8051 | Mention of 'intuition' in morality means something has gone wrong with the argument [MacIntyre] |
| 8048 | When 'man' is thought of individually, apart from all roles, it ceases to be a functional concept [MacIntyre] |
| 8035 | In trying to explain the type of approval involved, emotivists are either silent, or viciously circular [MacIntyre] |
| 8037 | The expression of feeling in a sentence is in its use, not in its meaning [MacIntyre] |
| 8040 | Emotivism cannot explain the logical terms in moral discourse ('therefore', 'if..then') [MacIntyre] |
| 8042 | Nowadays most people are emotivists, and it is embodied in our culture [MacIntyre] |
| 8058 | Maybe we can only understand rules if we first understand the virtues [MacIntyre] |
| 7097 | Virtue is secondary to a role-figure, defined within a culture [MacIntyre, by Statman] |
| 8043 | Characters are the masks worn by moral philosophies [MacIntyre] |
| 8061 | If morality just is emotion, there are no external criteria for judging emotions [MacIntyre] |
| 8038 | Since Moore thinks the right action produces the most good, he is a utilitarian [MacIntyre] |
| 8050 | There are no natural or human rights, and belief in them is nonsense [MacIntyre] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 8055 | If God is omniscient, he confronts no as yet unmade decisions, so decisions are impossible [MacIntyre] |